| Abstract [eng] |
This thesis investigates the hierarchy of Baire functions, a classification introduced by René-Louis Baire in 1899 to extend the study of "well-behaved" functions beyond continuity. Starting from continuous functions (Baire class 0), the hierarchy iteratively defines class n functions as pointwise limits of class (n−1) functions, providing a framework to describe discontinuous functions arising in analysis, such as solutions to differential equations. We explore fundamental properties of Baire functions, including characterization theorems, and analyze concrete examples to determine their respective classes. Our original contribution lies in the systematic study of several functions, employing methods such as continuity set analysis, limit constructions, and applications of Baire’s theorems. The results highlight the versatility of Baire’s hierarchy in classifying functions with complex limit behaviors. |
